Precalculus: Mathematics for Calculus

This paragraph introduces pre-calculus as an intriguing and challenging math class prevalent in the U.S. The speaker acknowledges the debate over whether to consider it a subject or a class, referencing a friend's opinion that it's essentially algebra and trigonometry with additional topics. The paragraph discusses the difficulty of the course, the speaker's personal experience of not achieving the expected grade, and suggests online courses or books as learning methods. A specific book recommendation is given, 'Pre-calculus Mathematics for Calculus' by Stuart Redland and Watson, which is praised for its comprehensive content, including more material than typically covered in college-level courses. The paragraph also highlights the book's authorship by well-known mathematicians, including James Stewart, famous for his influential calculus textbook.

The second paragraph delves into the specifics of the pre-calculus textbook 'Pre-calculus Mathematics for Calculus' by Redland and Watson, providing an overview of its contents. It starts with fundamental algebra topics like real numbers and functions, then progresses to more complex subjects such as polynomial and rational functions, exponential and logarithmic functions, and trigonometry. The speaker emphasizes the book's challenging problems and its coverage of topics not typically found in college algebra courses, such as analytic trigonometry, systems of equations, inequalities, and analytic geometry. The paragraph also mentions sequences and series, counting and probability, and a unique section on limits as a preview of calculus. The speaker appreciates the book's modern layout, clear explanations, and ample exercises with solutions, considering it a valuable resource for anyone studying pre-calculus. However, the paragraph concludes by noting the absence of certain topics, such as conic sections, which were not covered in the speaker's own pre-calculus course.

In this final paragraph, the speaker reflects on the value of a comprehensive pre-calculus textbook, arguing that despite the common complaint about the high cost of math books, they are priceless due to the wealth of knowledge they contain. The speaker admires the effort required to produce such a book and believes it is worth the investment. They also briefly touch upon the additional learning resources available, such as online courses on their website, mathsourcer.com, which are hosted on the Udemy platform. The speaker encourages the use of their provided links for potential cost savings and invites non-subscribers to subscribe for more content. The paragraph concludes with an acknowledgment of the difficulty of pre-calculus and mathematics in general, emphasizing the need for time and effort to master the subject, and ends with a note of encouragement to continue engaging with mathematics.